2025 BDS PRELIMS P2 Q8

The diagram shows part of the curve \(y=\frac{10}{12-x}-1\) passing through the point \(P(2k,k-1)\), where \(k\) is a constant. The curve meets the \(x\)-axis at the point \(X\). The tangent and normal at \(P\) meet the \(x\)-axis at the points \(T\) and \(N\) respectively.

1. Find the equation of the normal at \(P\).[6]
2. Find the exact area of the shaded region.[6]